Is the Universe Infinite or Finite?

Is the Universe Infinite or Finite? I was having that debate with a friend of mine today. My position was that it is finite because it is expanding. My logic was that the fact that is expanding indicates that it must be finite, because how could something be infinite and getting bigger?

His position was that it was infinite though he couldn't really explain why he thought that. (to give you some context, he also believes his daily horoscope offers him meaningful guidance and that aliens built the pyramids).

You may have guessed by now that neither one of us are physicists, so to settle the argument, I proposed that we contact an expert.

Confident of my correctness, I suggested to my buddy that we should have friend of this here site @seanmcarroll (the brilliant physicist and author of "From Eternity to Here") give us an answer.

I tweeted at Sean the subject line of this thread and he was kind enough to tweet me back in a matter of minutes. He said:

"Nobody knows. Sometimes that's the answer."

He then tweeted

"There may not even be an answer. de Sitter space (e.g.) can be finite or infinite depending on how you slice it."

So not wanting to badger Sean with follow up questions, I ask you: If we know the Universe is continually expanding (which to me suggests that it has a finite size that is increasing), how can it be labeled as anything other than finite?

Replies to This Discussion

You haven't told us anything about the physical universe there. You've just added more mathematical paradox to the paradoxes of Zeno (an arrow has to go half the distance to its target, then half that distance, then half that distance, and so on, never reaching its target).

Mathematics is a way of talking about reality, it isn't reality itself. When math sticks to reality (basing its calculations on measurements and other real values), paradoxes don't happen. When it is just thought problems, paradoxes are possible.

Does Infinity exist? In the literature the overwhelming answer to this question by the scientific community is yes... on paper. It is interesting to consider that in spite of a prolonged search for infinity in nature, it remains elusive. Although the importance of the concept of infinity in the field of mathematics is indisputable, ironically, it represents perhaps the most compelling example of a mathematical constructs that is “true” yet non existent in reality. (source)

As a matter of fact, space isn't infinitely divisible except in principle, mathematically. In math you can divide a photon into halves and quarters and so on to infinity, but try it in reality. At the smallest level, the physicists tell us that space is granular and seething.

Most likely conceptually, the matter that emerged in The Big Bang did come from somewhere. Another dimension? From one "brane" bumping into another? You and I will never know.

I don't need to know. What would I do with the answer? That doesn't mean I wouldn't like to know.

I gave three examples of different types of infinity two of which I think I did well enough for a non-math types to understand. I did ask what was meant by finite. I could have asked what is meant by infinite as you come back asking if it is infinite without describing what kind of infinite you are asking about. The answer is different depending upon what you mean by the question.

In terms of time from the present to bang time there are a finite numbers of "years" intervening. But what do you mean by expanding. The origin of the universe is at the present time every place in the universe.We can assign a unique number to every place in the universe with a value between 0 and 1. Or in the extremely in a range from 0 to an infinitely small number greater than zero.

But all the places are separated by time. In that sense we ARE now and always have been at the edge of the universe. There is no PLACE to expand into. There is only time continuing to separate places. Thus a different dimension something like entropy is the one coequal with the three space dimensions. This means every system has a different entropy. Reduce an object to zero entropy and it can travel forward in time unchanged forever.

Now I do not claim to have a definitive answer. I simply presented a fraction of the background that goes into the question hoping it helps you get a betting handle on the issues.

Myself I think time has to go as a co-equal dimension with space. It does not exist in quantum mechanics and although I am partial to relativity I don't think it will survive in its current form. Consider good old string theory. Four regular dimension and ten (or whatever they are up to today) tightly looped and unobservably small others. I have been trying to conceive of it as three space dimensions with one called time that is fairly large and observable locally with whatever others are needed after that change is made.

However I can't my head around that conceptually to convince myself to spend a year or three learning the math of string theory. So rest assured I will never be in a position to claim this idea is correct.

I think both of us are showing that we lack the language to meaningfully examine and talk about such things as infinity and finiteness. These concepts are inventions of mathematics. Pi has more real world meaning than infinity.

However, the physicists tell us that space isn't empty and has a texture and a constant activity going on at the deepest level, so there is something out there beyond the furthest-out photon for it to travel into. Whether space goes on forever (whatever that means) or whether it's a field like the field of a magnet that goes out so far but gets weaker the further out one goes, who knows?

When I was a kid, I thought of God as a wizard bent over a crystal ball (which contained the Universe) The kid in me used to think, "Where is God standing? What's behind him?"In my HS educated mind, I've always considered when the scientists say the Universe is expanding, they're talking about the matter they see expanding away from what they consider the center, or whatever. But the Universe itself, has to be infinite. If it's not, what lies beyond it? What lies outside of where the Universe stops? If you think of the room you're in as the Universe, and you walk all the way over to the wall where the room/Universe stops, what's on the other side of the wall? And if there's 'nothing' outside of the Universe...how big is the nothing? How much further does nothing go? Does the nothing just go on forever? Then 'nothingness' is infinite. If you can imagine reaching the furthest point, once you've reached it, there will ultimately be another point past it; there's logically always a yet further point to be reached. IMHO, the Universe is 'definitely' infinite.

You're asking me? I'm not sure that we, limited by our senses (or lack of senses) even have words to describe these things. Perhaps the universe creates space as it goes. Perhaps it's like a sphere where if you set off in a straight line you end up where you started. Space isn't empty and seems to be a substance of sorts, being compressible and stretchable by gravity, but does it go on forever or does it peter out somewhere out there? I don't think we'll ever know.

We are still apes, regardless of how we view ourselves, and I believe that there are numbers out there that are just so large, that our brains aren't yet sufficiently evolved to grasp them, and so we call them, "infinite." Possibly some actually are, but equally possibly, they are simply, as yet, beyond our comprehension.

"Infinity" is a purely conceptual construct, like zero. It's a child of mathematics. It's kind of a meaningless term in real life because (a) there's probably no way to prove a real infinity and (b) there's really no way to wrap one's head around the idea.